The relationship between multi-objective robustness concepts and set-valued optimization

详细信息    查看全文

• 作者：Jonas Ide ; Elisabeth K?bis ; Daishi Kuroiwa…
• 关键词：robust optimization ; multi ; objective optimization ; scalarization ; vectorization ; set ; valued optimization
• 刊名：Fixed Point Theory and Applications
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：315 KB
• 参考文献：1. Stewart, T, Bandte, O, Braun, H, Chakraborti, N, Ehrgott, M, G?belt, M, Jin, Y, Nakayama, H, Poles, S, Di Stefano, D Real-world applications of multiobjective optimization. In: Branke, J, Deb, K, Miettinen, K, Slowinski, R eds. (2008) Multiobjective Optimization: Interactive and Evolutionary Approaches. Springer, Berlin, pp. 285-327 CrossRef
  2. Scott, EM, Saltelli, A, S?rensen, T (2000) Practical experience in applying sensitivity and uncertainty analysis. Sensitivity Analysis. Wiley, Chichester, pp. 267-274
  3. Birge, JR, Louveaux, FV (1997) Introduction to Stochastic Programming. Springer, New York
  4. Kouvelis, P, Yu, G (1997) Robust Discrete Optimization and Its Applications. Kluwer Academic, Dordrecht CrossRef
  5. Ben-Tal, A, El Ghaoui, L, Nemirovski, A (2009) Robust Optimization. Princeton University Press, Princeton
  6. Fischetti, M, Monaci, M Light robustness. In: Ahuja, RK, Moehring, R, Zaroliagis, C eds. (2009) Robust and Online Large-Scale Optimization. Springer, Berlin, pp. 61-84 CrossRef
  7. Liebchen, C, Lübbecke, M, M?hring, RH, Stiller, S The concept of recoverable robustness, linear programming recovery, and railway applications. In: Ahuja, RK, M?hring, RH, Zaroliagis, CD eds. (2009) Robust and Online Large-Scale Optimization. Springer, Berlin
  8. Klamroth, K, K?bis, E, Sch?bel, A, Tammer, C (2013) A unified approach for different concepts of robustness and stochastic programming via nonlinear scalarizing functionals. Optimization 62: pp. 649-671 CrossRef
  9. Goerigk, M, Sch?bel, A (2011) A scenario-based approach for robust linear optimization. Proceedings of the 1st International ICST Conference on Practice and Theory of Algorithms in (Computer) Systems (TAPAS). Springer, Berlin, pp. 139-150 CrossRef
  10. Soyster, AL (1973) Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper. Res 21: pp. 1154-1157 CrossRef
  11. Ben-Tal, A, Nemirovski, A (1998) Robust convex optimization. Math. Oper. Res 23: pp. 769-805 CrossRef
  12. Deb, K, Gupta, H (2006) Introducing robustness in multi-objective optimization. Evol. Comput 14: pp. 463-494 CrossRef
  13. Branke, J Creating robust solutions by means of evolutionary algorithms. In: Eiben, EA, B?ck, T, Schenauer, M, Schwefel, H-P eds. (1998) Parallel Problem Solving from Nature - PPSNV. Springer, Berlin, pp. 119-128 CrossRef
  14. Barrico, C, Antunes, CH (2006) Robustness analysis in multi-objective optimization using a degree of robustness concept. IEEE Congress on Evolutionary Computation. pp. 1887-1892
  15. Steponavi??, I, Miettinen, K: Survey on multiobjective robustness for simulation-based optimization. Talk at the 21st International Symposium on Mathematical Programming, August 19-4 2012, Berlin, Germany (2012)
  16. Witting, K: Numerical algorithms for the treatment of parametric multiobjective optimization problems and applications. PhD thesis, Universit?t Paderborn, Paderborn (2012)
  17. Kuroiwa, D, Lee, GM (2012) On robust multiobjective optimization. Vietnam J. Math 40: pp. 305-317
  18. Ehrgott, M, Ide, J, Sch?bel, A (2014) Minmax robustness for multi-objective optimization problems. Eur. J. Oper. Res.
  19. Kuroiwa, D, Lee, GM: On robust convex multiobjective optimization. J. Nonlinear Convex Anal. (2013, accepted)
  20. Eichfelder, G, Jahn, J (2012) Vector optimization problems and their solution concepts. Recent Developments in Vector Optimization. Springer, Berlin, pp. 1-27 CrossRef
  21. Kuroiwa, D (1999) Some duality theorems of set-valued optimization with natural criteria. Proceedings of the International Conference on Nonlinear
• 刊物主题：Analysis; Mathematics, general; Applications of Mathematics; Differential Geometry; Topology; Mathematical and Computational Biology;
• 出版者：Springer International Publishing
• ISSN：1687-1812

文摘

In this paper, we discuss the connection between concepts of robustness for multi-objective optimization problems and set order relations. We extend some of the existing concepts to general spaces and cones using set relations. Furthermore, we derive new concepts of robustness for multi-objective optimization problems. We point out that robust multi-objective optimization can be interpreted as an application of set-valued optimization. Furthermore, we develop new algorithms for solving uncertain multi-objective optimization problems. These algorithms can be used in order to solve a special class of set-valued optimization problems.